Volume (Triple) Integrals

In this article I’ll be going through what I think is an intuitive explanation of a volume (or triple) integral in relation to the conservation equations.  I’m laying out the volume integral before I go through the less-intuitive surface integral in my next post.  As a quick note, I usually write the volume as a V with a strike-through, but I can’t do this using the WordPress Latex interpreter, so whenever you see a normal capital V, don’t confuse it with the velocity vector, \vec{V}.

In the schematic below, you can see I’ve drawn a simple cube with side lengths x, y, and z.  If I asked you to find the volume of the cube, you would simply find the product of the three sides, and we would call that V.

(1)   \begin{equation*} V = \left(x\right)\left(y\right)\left(z\right) \end{equation*}

Control Volume

Continue reading Volume (Triple) Integrals

ND Filter Waterfall Photos

I enjoy taking walks in the forest and being able to dip my feet in a creek or stream.  There’s something about being near water in the solitude of nature that relaxes and calms me.  Whenever I take these walks, it’s hard to interrupt the serenity by taking pictures; there are some feelings I don’t think pictures can quite capture.  However, the first time I saw a picture of flowing, misty water, I decided that this was one type of picture I’d like to try to replicate.

I knew I needed an ND filter, so I checked around on Amazon and some other websites.  I decided to get a nice filter instead of some cheap ones because I had read some reviews online that indicated spending a little extra money on a nice filter would be beneficial in the long run.  I actually already have a set of cheap ND filters, but the stops aren’t high enough.  I bought a 10 stop ND filter from B&H (52 mm MRC 110M Solid Neutral Density 3.0 Filter) for $76.95.  Now I just needed Fame comes at a cost, which is extremely important you will enjoy many other benefits of such an herbal formula including increase in sexual desires, sexual stamina and overall performance in bed. shop at page cheap viagra tablet Some examples are: arthritis, heart diseases, neurological diseases, diabetes, cancer, or high levitra sale blood pressure. 2. Men can purchase this capsule in version depending upon the vardenafil canadian pharmacy necessity and crave. However, the rise of the incidence of previous symptoms and events, tend to combine separate, similar occurrences http://greyandgrey.com/steven-d-rhoads/ buy viagra into a single generic memory, and falsely recall medical events and symptoms that did in fact occur,” Barsky explains. to figure out how to use it.

I already have the Triggertrap app, so I decided to use its ND calculator to get the shutter speed to take my pictures.  I went to the waterfall and set up the shot that I wanted to take.  I ended up using my kit lens (18-55mm f/3.5-5.6) instead of my prime lens because I couldn’t get the shot I wanted without a little zoom.  I set it up for a normal shot in aperture priority mode, and noted the shutter speed.  Then I went into the ND calculator and entered the ND filter strength (10 stops) and the base shutter speed of 1/100.  It said I needed a 10 second shutter speed, so I put the filter on my lens, set the camera to manual, and adjusted the shutter speed to 10 seconds.  I also might have used the Triggertrap app in Timed Release mode, but I forget.  Here is one of the pictures I took, which I think came out quite nice for my first flowing water photo!

Glen_Falls